What is the integral of 7x^2ln(x) ?

The integral of 7x^2ln(x) is 7(1/3 x^3ln(x)-(x^3)/9)+C

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integral of 7x^2ln(x)

\int 7 x^{2} ln (x) d x

7 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

Solution steps

\int 7 x^{2} ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int x^{2} ln (x) d x

Apply Integration By Parts

: \frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x

= 7 (\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x)

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= 7 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

Add a constant to the solution

= 7 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

\frac{d y}{d x}, arctan (x y) = arcsin (4 x + 4 y), (0, 0)

e^{7 t} sin^{2} (t)

\frac{d P}{d t} = k P^{1.01}

\int \frac{( x - 3 )}{x ^{3} + x ^{2}} d x

\int 4 x^{2} - sin (x) d x

What is the integral of 7x^2ln(x) ?
The integral of 7x^2ln(x) is 7(1/3 x^3ln(x)-(x^3)/9)+C